As @d parolin pointed out, the figure generated by matplotlib will need to be saved before being rendered by the HTML. In order to serve images in flask by HTML, you will need to store the image in your flask file directory:
static/
images/
plot.png --> store plots here
templates/
Therefore, in your application, use plt.savefig:
@app.route('/test')
def chartTest():
lnprice=np.log(price)
plt.plot(lnprice)
plt.savefig('/static/images/new_plot.png')
return render_template('untitled1.html', name = 'new_plot', url ='/static/images/new_plot.png')
Then in untitled1.html:
<p>{{ name }}</p>
<img src={{ url}} alt="Chart" height="42" width="42">